I was trying to solo Apollyon SE recently, and took my DNC. Everything is fine until floor 2 cleared. And at floor 3 I was smashed by the corse NM since I forgot Mensur Epee is a piercing type damage. Then I re-looked again the list at FFXIAH; It seems all the swords for DNC out there is rapier type (i.e. piercing damage type).

Lex Talionis seems to be the highest damage slashing type sword Dnc can use(Unless Talekeeper/Sagasinger are actually slashing as well). Bit to much effort to get for the one reason you'd ever need it though, so Tutelary may the easiest option, though it's not really commonly sold on Cerberus anymore.

Colichemarde may be slashing damage as well, since Blm is included on the usable jobs(All Bilbo type swords are slashing, and almost all include Blm on the list). Not seeing anything on wiki about it though, so no telling if it is slashing or piercing.

Another non-sword option for slashing damage is the Chiroptera Dagger, which drops from Tres Duendes in Phomiuna Aqueducts. However, that's tied to a 21-24 hour repop so it may/may not require some effort. Uchi's suggestions are excellent, so hopefully you could pick one of those swords up.

I actually use Vampiric Claws for slashing damage. I'm I think it's probably better than Chiroptera (because H2H base damage goes up with skill), but I suspect it's worse than Lex Talonis.

You could also use a blunt H2H weapon for that Limbus floor, particularly applicable to those who have H2H skill already from MNK or PUP. Not a lot of fantastic options, but for the limited purpose of that single Limbus floor it's a viable choice. Eyra Baghnakhs are kinda expensive for the limited purpose, otherwise you're talking 75cap weapons: Destroyers, Wagh Baghnaks, Koenigs Knuckles, etc.